The
hamming distance between two code vectors is equal to the number of elements in
which they differ. For example, let the two code words be,

X =
(11100) and Y= (11011)

D= 2
These two code words differ in second and third bits. Therefore the hamming
distance between X and Y is two.

5.What is convolution code? How is it different from
block codes?

Fixed
number of input bits is stored in the shift register & they are combined
with the help of mod 2 adders. This operation is equivalent to binary
convolution coding.

6.State any four desirable properties of line code

·The PAM signal should have adequate timing content,

·The PAM signal should immune to channel noise and
interference

·The PAM signal should allow error detection and
error correction

·The PAM signal should be transparent to digital
data being transmitted

7.Find the hamming distance 101010 and 010101.If the
minimum hamming distance of a (n,k) linear block code is 3, what is its minimum
hamming weight?

d(x1,x2)=x1
exor x2 =111111

d(x1,x2)=6

Dmin=3
then Wmin=dmin=3

8. What is meant by syndrome of linear block code?

The non
zero output of the produce YHT is called syndrome & it is used to detect
errors in y. Syndrome is denoted by S & given as,

S=YHT

9. What is convolutional code? Explain the
fundamental difference between block codes and convolutional codes.

Block
codes takes‟k‟ number of bits simultaneously form „n‟-bit code vector. This
code vector is also called block. Convolutional code takes one message bits at
a time and generates two or more encoded bits. Thus convolutional codes
generate a string of encoded bits for input message string.

10. What is hamming distance?

The
hamming .distance .between .two code vectors .is equal to the number .of
elements in which they differ. For example, let the two code words be,

X = (101)
and Y= (110)

These
.two code words differ in second and third bits.Therefore .the .hamming
distance between X and Y is two.

11. Define code efficiency.

The code
efficiency is the ratio of message bits in a block to the transmitted bits for
that block by the encoder i.e.,

Code
efficiency= (k/n)

k=message
bits

n=transmitted
bits.

12.What are
the error detection and correction capabilities of hamming codes ?

The
minimum distance (dmin) of hamming codes is „3‟. .Hence it can be used to
detect double errors or correct single errors. Hamming codes are basically
linear block codes with dmin =3.

13.What is
meant by linear code?

A code is
linear if modulo-2 sum of any two code vectors produces another code vector.
This means any code vector can be expressed as linear combination of other code
vectors.

14. What is meant by cyclic codes?

Cyclic
codes are the subclasses of linear block codes. They have the property that a
cyclic shift of one codeword produces another code word.

15. How syndrome is calculated in Hamming codes and
cyclic codes?

In
hamming codes the syndrome is calculated as,

S=YHT

Here Y is
the received and H.is the transpose of parity check matrix

16. What is difference between block codes and
convolutional codes?

Block
codes takes‟k‟ .number of bits simultaneously form „n‟-bit .code vector. This
code vector is also called block. Convolutional code takes one message bits at
a time and generates two or more encoded bits. Thus convolutional codes
generate a string of encoded bits for input message string.

ERROR CONTROL CODING – IMPORTANT TERMS

Properties of cyclic codes:

Linearity property

The sum
of any two code word is also a valid code word

Cyclic property

Every cyclic
shift of a valid code vector produces another valid code vector.

Hamming distance.

The
hamming distance between two code vectors is equal to the number of elements in
which they differ. For example, let the two code words be,

X = (101)
and Y= (110) These two code words differ in second and third bits. Therefore
the hamming distance between X and Y is two.

Transparency with respect to line codes:

The line
code is said to be transparent if the synchronization between the transmitter
and receiver is maintained for any type of input data sequence.

Hamming distance:

The
hamming distance between two code vectors is equal to the number of elements in
which they differ. For example, let the two code words be,

X =
(11100) and Y= (11011)

D= 2
These two code words differ in second and third bits. Therefore the hamming
distance between X and Y is two.

Convolution code:

Fixed
number of input bits is stored in the shift register & they are combined
with the help of mod 2 adders. This operation is equivalent to binary
convolution coding.

Properties of line code:

·The PAM signal should have adequate timing content,

·The PAM signal should immune to channel noise and
interference

·The PAM signal should allow error detection and
error correction

·The PAM signal should be transparent to digital
data being transmitted

Syndrome of linear block code:

The non
zero output of the produce YHT is called syndrome & it is used to detect
errors in y. Syndrome is denoted by S & given as,

S=YHT.

Convolutional code:

Block
codes takes‟k‟ number of bits simultaneously form “n”-bit code vector. This
code vector is also called block. Convolutional code takes one message bits at
a time and generates two or more encoded bits. Thus convolutional codes
generate a string of encoded bits for input message string.

Code efficiency:

The code
efficiency is the ratio of message bits in a block to the transmitted bits for
that block by the encoder i.e.,

Code
efficiency= (k/n) k=message bits

n=transmitted
bits.

Error detection and correction capabilities of
hamming codes:

The
minimum distance (dmin) of hamming codes is „3‟. .Hence it can be used to
detect double errors or correct single errors. Hamming codes are basically
linear block codes with dmin =3.

Linear code:

A code is
linear if modulo-2 sum of any two code vectors produces another code vector.
This means any code vector can be expressed as linear combination of other code
vectors.

Cyclic codes:

Cyclic
codes are the subclasses of linear block codes. They have the property that a
cyclic shift of one codeword produces another code word.

syndrome is calculated in Hamming codes and cyclic
codes:

In
hamming codes the syndrome is calculated as,

S=YHT

Here Y is
the received and H.is the transpose of parity check matrix

Block codes and convolutional codes:

Block
codes takes ‟k” .number of bits simultaneously form “n”-bit .code vector. This
code vector is also called block. Convolutional code takes one message bits at
a time and generates two or more encoded bits. Thus convolutional codes
generate a string of encoded bits for input message string.